Campus Units
Mathematics, Electrical and Computer Engineering
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
5-15-2016
Journal or Book Title
Linear Algebra and its Applications
Volume
497
First Page
66
Last Page
87
DOI
10.1016/j.laa.2016.02.018
Abstract
The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distance spectrum of G. We determine the distance spectra of double odd graphs and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Copyright Owner
Elsevier Inc.
Copyright Date
2016
Language
en
File Format
application/pdf
Recommended Citation
Aalipour, Ghodratollah; Abiad, Aida; Berikkyzy, Zhanar; Cummings, Jay; De Silva, Jessica; Gao, Wei; Heysse, Kristin; Hogben, Leslie; Kenter, Franklin H.J.; Lin, Jephian C.H.; and Tait, Michael, "On the Distance Spectra of Graphs" (2016). Mathematics Publications. 57.
https://lib.dr.iastate.edu/math_pubs/57
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Signal Processing Commons
Comments
This is a manuscript of an article published as Aalipour, Ghodratollah, Aida Abiad, Zhanar Berikkyzy, Jay Cummings, Jessica De Silva, Wei Gao, Kristin Heysse et al. "On the distance spectra of graphs." Linear Algebra and its Applications 497 (2016): 66-87. DOI: 10.1016/j.laa.2016.02.018. Posted with permission.